Ronnie Brown : Groupoids and crossed objects in algebraic topology. PostScript file. Introduction. Groupoids in homotopy theory. The search for higher order versions of the fundamental group in homotopy theory. Whitehead’s work on crossed modules. The 2-dimensional Van Kampen theorem. Computation with crossed modules and second relative homotopy groups. Preliminaries on double groupoids. The homotopy double groupoid of a triple of spaces. The 2-dimensional Van Kampen theorem. The category of crossed complexes. Homotopies of morphisms of crossed complexes. Relations with chain complexes with operators. Cohomology classes. Further work.